The region of the electromagnetic spectrum between the wavelengths of 10 .mu.m and 500 .mu.m, generally known as the far-infrared, is largely unexplored. There are few detectors, and even fewer sources of bright radiation, in this region. Hence it is not surprising that there are no photometric calibration standards that work in the far infra-red. At visible wavelengths, opalescent glass functions as a calibration standard by diffusely transmitting the incident light equally in all directions, i.e. isotropically. This invention functions at far-infrared wavelengths by diffusely reflecting normally incident radiation equally in all directions. Further, the photometric value of that isotropic reflectance is constant between the wavelengths of 5 and 100 .mu.m. Thus, the fact that the reflectance by this invention does not depend on either wavelength or the direction of reflection makes it a valuable photometric standard for the far-infrared, where, as noted, there are no existing standards. This invention may also be used as a standard in the infrared region of the spectrum.
For a surface to diffusely reflect very long wavelengths of far-infrared radiation in an efficient manner, the surface must be very rough, the features on it which are responsible for its roughness must be randomly oriented and uniformly distributed, and the surface must neither absorb nor transmit any of the incident radiation. It is a well known principle of optics that when the dimensions of an object or feature are about as large as the wavelength of the radiation involved, very significant diffraction or scattering effects occur. In particular, when the average size of a surface feature is larger than a wavelength of the incident radiation, the incident photons can "see" the random orientation of the individual features and can transfer that random distribution into the diffuse reflectance of the entire surface as a random distribution of reflected light rays. A random distribution of reflected light is the same in all directions, hence it is isotropic. Isotropic reflectance is considered to be perfectly diffuse because it has no enhancement or peak in the specular direction. Another term for perfectly diffuse or isotropic is Lambertian. In the absence of any absorption or transmission by a surface, its isotropic reflectance has a simply calculated value of 1/.pi. sr.sup.-1, and, as long as the wavelength remains smaller than the average size of a surface feature, that isotropic reflectance is independent of the value of the wavelength.
A surface that neither absorbs nor transmits any of the incident light, but reflects all of it, is considered to be a perfect reflector. At far-infrared wavelengths, most metals are perfect reflectors.
The average size of a surface facet is about twice the r.m.s. roughness, .sigma., of the surface, where .sigma. is defined as the root-mean-squared variation of surface height from the average height of the surface (.sigma. is approximately related to the arithmetic average roughness, Ra, by .sigma. .apprxeq. 1.11 .times. Ra). Thus for wavelengths of radiation, .lambda., to be smaller than the individual facets of a randomly rough surface, the condition is .lambda..ltoreq.2.sigma.. A bidirectional reflectance distribution function (BRDF) to describe diffuse reflectance has been defined by F. E. Nicodemus and others (NBS Monograph #160, October 1977, U.S. Dept. of Commerce) as the bidirectional reflectance per unit projected detector solid angle. The value of the BRDF of an isotropic perfect reflector is 1/.pi. sr.sup.-1, and as noted above this value is independent of both the direction of reflection and the wavelength as long as .lambda.&lt;2.sigma..
The directional reflectance actually measured by a detector with a projected detector solid angle of .OMEGA..sub.d Cos.crclbar..sub.s, is given in terms of the BRDF by EQU R(.lambda.,.crclbar..sub.s)=BRDF(.lambda.,.crclbar..sub.s).OMEGA..sub.d Cos.crclbar..sub.s.
Here .crclbar..sub.s indicates the angle reflection or scatter. If the reflecting surface is an isotropic perfect reflector, and .lambda.&lt;2.sigma., then the measured diffuse reflectance is EQU R(.crclbar..sub.s)=(1/.pi.).OMEGA..sub.d Cos.crclbar..sub.s
the value of which is independent of wavelength and has only a very slight dependence on angle introduced by the obliqueness of the detector to the surface. Current theories of diffuse reflection (Beckman & Spizzichino, "The Scattering of Electromagnetic Waves from Rough Surfaces," Artech House Inc., Norwood Mass., 1987) indicate that although the direction reflectance is not isotropic at wavelengths longer than 2.sigma., it will still be largely diffuse at wavelengths as long as 8.sigma..
Diffuse reflectors for shorter wavelength radiation in the infrared region (from 0.8 .mu.m to 10 .mu.m) have been manufactured in a number of ways. Generally, diffuse reflectors are made by taking a reflective surface and roughening one of its faces. One method of manufacture involves sprinkling powders on a flat surface and gluing the powders to the surface. A second method involves grinding or blasting a metal or glass surface to achieve the necessary roughness for diffusely reflecting infrared wavelengths. A third method is to dimple an aluminum surface with a regular hexagonal array of approximately 1/64 inch (400 .mu.m) diameter holes. These methods suffer from the ability to diffusely reflect far infrared wavelengths of 15 .mu.m or longer.
The primary disadvantages of the above methods of roughening a reflective surface is that they either do not make the surface rough enough or they do not make the roughness random enough to enable the surface to function as an isotropic diffuse reflector for far-infrared wavelengths. If the surface is not rough enough (i.e., .lambda. is larger than 2.sigma.) the reflectance will not be perfectly diffuse and it will have an enhancement or peak in the specular direction which gets longer at longer wavelengths. If the roughness is non-random, the non-randomness will create diffraction effects which favor particular off-specular directions of reflection, thus making the diffuse reflectance non-isotropic.
Other general methods for roughening a surface include electric discharge machining (EDM). U.S. Pat. No. 3,754,873 (Bills et al.) discloses a cold rolled sheet having a roughened surface formed by projections of such shape and arrangement that the visual appearance of the surface of the sheet is relatively constant. This sheet is disclosed as having an r.m.s. roughness .sigma. between 0.56 and 11.1 micrometers (Ra between 20 and 400 microinches). The steel sheet so produced is taken up on a coiler and there is no disclosure of the sheet being utilized for optical purposes, e.g., as a reflector for light at any wavelength.
U.S. Pat. No. 4,589,972 (Pompea et al.) discloses a coating which is optically black in the infrared region, i.e. one that absorbs the infrared part of the spectrum of light. This absorption is provided by the anodization and dyeing process, disclosed in U.S. Pat. No. 4,111,762, applied to a substrate that has a random series of "surface modifications" having an approximate width of about 100 microns and a depth of about 50 microns. The Pompea et al patent discloses that one method of creating such surface modifications is by an EDM process, but the patent does not suggest the use of such an EDM process for producing a reflective surface.
Other U.S. patents of general interest include 4,203,028 (Brumann); 4,655,136 (Reiss et al.); and 3,669,867 (Adachi) which disclose various methods of etching sheets.